President Barack Obama and House Speaker John Boehner moved closer to a deal on tax increases and spending cuts late Monday, though some details remain to meet an end-of-the-year deadline.

Obama administration officials and House Republicans acknowledge that the two sides are closer than they have been to a compromise that averts the so-called fiscal cliff.

The president offered a new proposal that raises taxes for those earning more than $400,000, up from the $250,000 income level he had been demanding. His proposal also reduces the amount of new taxes he is demanding to $1.2 trillion over the next 10 years, down from $1.4 trillion, and applies a less-generous measure of inflation to Social Security and other programs.

The $2.4 trillion proposal offers an equal amount of revenue and spending cuts.

A source familiar with the negotiations said late Monday that it was not likely to be the last White House offer, but one that meets Republicans halfway on spending and revenues. A quarter of the spending reductions would be in health care, the source said. The proposal also would allow the debt limit to be increased for two years, with periodic votes in Congress.

But there is disagreement between the two sides on how to define the spending cuts and revenues.

"Any movement away from the unrealistic offers the president has made previously is a step in the right direction, but a proposal that includes $1.3 trillion in revenue for only $930 billion in spending cuts cannot be considered balanced,"' Boehner spokesman Brendan Buck said. “We hope to continue discussions with the president so we can reach an agreement that is truly balanced and begins to solve our spending problem."'

The news came after Obama and Boehner met behind closed doors for 45 minutes at the White House on Monday -- their third such meeting in a week.

Failure to reach a deadline by the end of the year would mean that $500 billion in tax increases take effect early next year, coupled with $109 billion in spending reductions, the first installment toward $1.2 trillion in cuts over two years.

Boehner offered late last week a plan that would include higher tax rates on millionaires, the first time he has known to have been specific about offering higher rates, according to multiple reports.

Congress returned to work Monday night, and plans to be in session throughout the week.